Parallel Lines 71Fb50

1. **State the problem:** We are given that angle one is congruent to angle two, and we need to prove that line $l$ is parallel to line $m$. 2. **Recall the relevant theorem:** If a transversal intersects two lines and the corresponding angles are congruent, then the two lines are parallel. 3. **Identify the angles:** Angle one and angle two are corresponding angles formed by the transversal intersecting lines $l$ and $m$. 4. **Given:** $\angle 1 \cong \angle 2$ 5. **Apply the Corresponding Angles Postulate:** Since the corresponding angles are congruent, lines $l$ and $m$ must be parallel. 6. **Conclusion:** Therefore, $l \parallel m$. This completes the proof that line $l$ is parallel to line $m$ based on the congruence of the corresponding angles.